1,2

Equivalently, Chowla function of n modulo n is congruent to 1.

If p=2^i-3 is prime, then 2^(i-1)*p is a member of the sequence. 650 is in the sequence, but is not of this form.

For 1 < n <= 134193152 this sequence has the property that if sigma(n)==2 (mod n) then sigma(n)==0 (mod n+1). It is not known if this holds in general, for there might be solutions of sigma(n)=3n+2 or 4n+2 or ... (Comments from Jud MccCranie and Dean Hickerson).

n | Sigma(n) produces the multiperfect numbers (A007691). It is an open question whether n | Sigma(n) - 1 iff n is a prime or 1. It is not known if there exist solutions to sigma(n) = 2n+1.

Sequence gives also the nonprime solutions to sigma(n)==0 (mod n+1 ) n>1 - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 05 2002

Sequence seems to give nonprime n such that the numerator of the sum of the reciprocals of the divisors of n equals n+1 (nonprime n such that A017665(n)=n+1). - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 04 2002

R. K. Guy, Unsolved Problems in Number Theory, B2.

sigma(650) = 1302 == 2 mod 650.

Do[If[Mod[DivisorSigma[1, n]-2, n]==0, Print[n]], {n, 1, 10^8}]

n such that A054013(n)=1.

Cf. A050414, A050415.

Sequence in context: A077757 A126859 A071334 this_sequence A088831 A063785 A135174

Adjacent sequences: A045765 A045766 A045767 this_sequence A045769 A045770 A045771

easy,nonn

Dan Hoey (Hoey(AT)aic.nrl.navy.mil)

More terms from Jud McCranie (j.mccranie(AT)comcast.net), Dec 22 1999. He says there are no other terms < 4290000000.